What happens when you stir a superfluid?

If I stir up some liquid helium in a container with an irregular shape, I’d expect to see a vortex break up into smaller and smaller vortices. Since liquid helium has no viscosity, I would also expect that the rotational inertia would be sustained in this process. So what happens as the vortices become vanishingly small? Do you eventually have pairs of atoms orbiting each other or does the inertia eventually transfer to the atomic nuclei?